The main objective of this project is to develop novel statistical methods for the analysis of cocaine relapse data. A particular interest is to understand the causes for the heterogeneity in cocaine relapse. Conventionally summary measures like percent of days abstinent and time to first relapse have been frequently used to characterize one's cocaine relapse pattern. However, these commonly used measures fail to utilize information that could be important to further distinguish the behaviors between subjects who share similar values of these measures. Moreover, they cannot describe the temporal trend of the data and thus prohibit the study of the relationship between relapse and time-varying variables such as craving/stress. The specific aims of this project are to: 1) derive informative measures for one's cocaine use behavior and use such measures to subtype one's cocaine relapse pattern;2) link one's cocaine relapse pattern to pretreatment variables including variables characterizing one's baseline cocaine use pattern and demographic variables like gender and age;3) understand the dynamic relationship between cocaine relapse and time-varying craving/stress levels after treatment;4) implement the developed statistical methods in user-friendly computer programs and make them available to the scientific com- munity. To achieve these aims, we will develop cutting-edge statistical methods covering several areas including functional data analysis, measurement errors, recurrent event processes and joint modeling of longitudinal outcomes and recurrent event processes. Statistical properties of these methods will be thoroughly investigated through both rigorous theoretical derivations as well as extensive simulations. Specifically, the proposed subtyping methods will enhance our understanding on the causes for cocaine relapse. This can in turn potentially inform the design of new individually targeted relapse prevention and pharmacological strategies to improve outcomes associated with cocaine dependence. Modeling the data as recurrent event processes al- lows us to make full use of the information available in one's relapse pattern and thus provides a more powerful way to detect any treatment effect. The proposed method to jointly model longitudinal outcomes and recurrent event processes allows us to assess the dynamic relationship between relapse and temporally varying variables such as craving/stress. A greater understanding of this relationship could lead to more effective treatment for cocaine abuse. In terms of statistical innovation, we for the first time introduce the novel concept of conducting functional data analysis for the mean and correlation structures of a stochastic process simultaneously, develop model-free methods to account for the measurement error when some predictors are derived from a stochastic process, and propose computationally efficient algorithms to jointly model longitudinal outcomes and recurrent event processes. PUBLIC HEALTH RELEVANCE: This project will develop novel statistical methods for the analysis of cocaine relapse data. These new methods can be used to help understand the causes for the heterogeneity in individual cocaine relapse patterns. This in turn can potentially inform the design of new individually targeted, more effective relapse prevention and pharmacological strategies to improve outcomes associated with cocaine dependence.